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Search: id:A111924
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| A111924 |
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Triangle of Bessel numbers read by rows. Row n gives T(n,n), T(n,n-1), T(n,n-2), ..., T(n,1) for n >= 1. |
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+0
7
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| 1, 1, 1, 1, 3, 0, 1, 6, 3, 0, 1, 10, 15, 0, 0, 1, 15, 45, 15, 0, 0, 1, 21, 105, 105, 0, 0, 0, 1, 28, 210, 420, 105, 0, 0, 0, 1, 36, 378, 1260, 945, 0, 0, 0, 0, 1, 45, 630, 3150, 4725, 945, 0, 0, 0, 0, 1, 55, 990, 6930, 17325, 10395, 0, 0, 0, 0, 0, 1, 66, 1485, 13860, 51975, 62370
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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T(n,k) = number of partitions of an n-set into k nonempty subsets, each of size at most 2.
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REFERENCES
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J. Y. Choi and J. D. H. Smith, On the unimodilty and combinatorics of Bessel numbers, Discrete Math., 264 (2003), 45-53.
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FORMULA
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The Choi-Smith reference gives many further properties and formulae.
T(n, k) = T(n-1, k-1) + (n-1)*T(n-2, k-1).
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EXAMPLE
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Triangle begins:
1
1 1
1 3 0
1 6 3 0
1 10 15 0 0
1 15 45 15 0 0
1 21 105 105 0 0 0
1 28 210 420 105 0 0 0
1 36 378 1260 945 0 0 0 0
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MATHEMATICA
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T[n_, 0] = 0; T[1, 1] = 1; T[2, 1] = 1; T[n_, k_] := T[n - 1, k - 1] + (n - 1)T[n - 2, k - 1]; Table[T[n, k], {n, 12}, {k, n, 1, -1}] // Flatten (* Robert G. Wilson v *)
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CROSSREFS
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A100861 is another version of this triangle. Row sums give A000085.
Sequence in context: A102765 A129684 A105147 this_sequence A100485 A143397 A137680
Adjacent sequences: A111921 A111922 A111923 this_sequence A111925 A111926 A111927
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 25 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Dec 09 2005
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